When Joe Kapp took over the football team at the University of California-Berkeley before the 1982 season, he wanted to impress upon his players the need to make sacrifices. So the coach made them a vow: He would forgo tequila until Cal won the Rose Bowl. Nearly three decades later, the 71-year-old is still waiting. "I've got the bottle right here," he says.

Talk of curses is uncommon in college football. Most of the great historical jinxes—the "please-let-them-win-before-I-die" kind—haunt the fans of professional teams, where a rotten owner can cripple a team for generations. The nature of college sports is that the players come and go, so every four years, there's a chance for a fresh start. At some point, if the school commits itself to winning, the pieces will fall into place and the fans' feeling of collective hopelessness will be relieved.

But then there's Cal. This once-powerful football program, a member of the elite Pac-10 conference, hasn't reached the coveted Rose Bowl since the 1958 season. No other conference school has been absent that long. (Arizona has never made it, but it only joined the conference in 1978.) Every time Cal comes close, something goes horribly, inexplicably wrong.

There was the time in 2006 when they had a key touchdown called back, the time in 2004 when poll voters turned against them, and the time in 2007 when quarterback Kevin Riley failed to stop the clock. Then came last Saturday, when the undefeated Bears, ranked No. 6 in the nation, faced unranked Oregon and lost by the shocking score of 42-3. "The Bears showed up in Oregon to take a stroll," says Mr. Kapp, "and they were on a freeway."

If the Bears can't win Saturday at home against No. 7 Southern California, they'll effectively be out of the Rose Bowl running again. "You'd see the collective psyche of the fan base collapse inward into the fetal position," says Cal alum Erik Johannessen, who expects to lose Saturday.

Going into the Oregon game, Cal was favored by a touchdown. Experts prattled on about how Oregon's offensive line was weak, its quarterback was inaccurate and Cal's star running back, Jahvid Best, would be hard to stop. But on a site called "Dr. Saturday," one Cal fan chimed in with what would prove to be the irrational truth. "Cal should win, but they won't," the commenter wrote. "Dunno why, dunno how, but they won't win."